3D Hermite Transform Optical Flow Estimation in Left Ventricle CT Sequences

Heart diseases are the most important causes of death in the world and over the years, the study of cardiac movement has been carried out mainly in two dimensions, however, it is important to consider that the deformations due to the movement of the heart occur in a three-dimensional space. The <mml:semantics>3D+t</mml:semantics> analysis allows to describe most of the motions of the heart, for example, the twisting motion that takes place on every beat cycle that allows us identifying abnormalities of the heart walls. Therefore, it is necessary to develop algorithms that help specialists understand the cardiac movement. In this work, we developed a new approach to determine the cardiac movement in three dimensions using a differential optical flow approach in which we use the steered Hermite transform (SHT) which allows us to decompose cardiac volumes taking advantage of it as a model of the human vision system (HVS). Our proposal was tested in complete cardiac computed tomography (CT) volumes ( 3D), as well as its respective left ventricular segmentation. The robustness to noise was tested with good results. The evaluation of the results was carried out through errors in forwarding reconstruction, from the volume at time t to timet+1 using the optical flow obtained (interpolation errors). The parameters were tuned extensively. In the case of the 2D algorithm, the interpolation errors and normalized interpolation errors are very close and below the values reported in ground truth flows. In the case of the 3D algorithm, the results were compared with another similar method in 3D and the interpolation errors remained below 0.1. These results of interpolation errors for complete cardiac volumes and the left ventricle are shown graphically for clarity. Finally, a series of graphs are observed where the characteristic of contraction and dilation of the left ventricle is evident through the representation of the 3D optical flow.